Answer :
Final answer:
Frederick and Lana evaluated the same numerical expression differently. Frederick's incorrect answer suggests he didn't follow the correct order of operations, while Lana's correct answer indicates she did. The correct evaluation involves performing operations inside the parentheses first, then subtracting.
Explanation:
In the given question, Frederick and Lana are evaluating the same numerical expression, but they are not following the same order of operations. In mathematics, the order of operations is important to ensure accurate calculation.
Frederick's incorrect answer of 51.5 suggests that he might have performed addition and subtraction from left to right without considering the parentheses first. On the other hand, Lana's correct answer of 59.1 indicates that she followed the correct order of operations, which is parentheses, multiplication/division, and then addition/subtraction.
To explain this in more detail, we can break down the correct evaluation step by step:
- Inside the first set of parentheses: 53.7 + 37.2 = 90.9
- Inside the second set of parentheses: 3 * 3 + 3.8 = 9 + 3.8 = 12.8
- Subtracting the result of step 2 from the result of step 1: 90.9 - 12.8 = 78.1
- Subtracting 8.6 from the result of step 3: 78.1 - 8.6 = 69.5
Therefore, the correct answer is 69.5, not 59.1.
Learn more about Order of operations
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Both people can be correct because of a little something called PEMDAS or the OOO (order of operations). In the first problem, the equation includes brackets and parentheses, doing 53.7+37.2 THEN 33+3.8 THEN subtracting them THEN subtracting 8.6 from that number, instead of doing 53.7+37.2 THEN subtracting 33 THEN adding 3.8 THEN subtracting 8.6. Doing certain parts of the equation first, dicated by the parentheses/brackets/braces, can change the final answer. The second expression has you going in order one by one, while the first has you doing groups of the equation at a time (neither are wrong or bad).
